Abstract
We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg L-functions attached to two cuspidal automorphic representations.
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Acknowledgements
The first author is supported by the National Key Research and Development Program of China (No. 2021YFA1000700) and NSFC (No. 12031008). The second author is supported by Postdoctoral Fellowship Program of CPSF. The authors are very grateful to the referees for the very careful reading of the manuscript and helpful suggestions.
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Communicated by Alberto Minguez.
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Lü, G., Ma, Q. Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions. Monatsh Math 204, 127–155 (2024). https://doi.org/10.1007/s00605-024-01952-4
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DOI: https://doi.org/10.1007/s00605-024-01952-4